Pinning two test particles at two different points in space, how can I calculate their spatial distance, when the geometry is given by the Schwarzschild metric?
Let's say particle 1 is pinned at $r=R$, $\theta=\frac \pi 2$, $\varphi = 0$ where $R$ is a positive radius bigger than the Schwarzschild radius and particle 2 is pinned at $r=R+L$, $\theta=\frac \pi 2$, $\varphi = 0$ where $L$ is also a positive constant.
What is now the spatial distance between the two particles?
Do I have to calculate the length of a geodesic from one particle to the other? Is this equal to the distance?